My advice is similar. It's worth having private insurance if you can afford it, as it makes a huge difference to waiting times, choice of consultants, and - being honest- better surroundings if you need admission.
Most policies have a 2-year rule, so they won't cover you for anything existing if it's occurred in the last 2 years.
They won't cover chronic conditions .
You can pay for private health as you need it. As PPs have said, a consultation can cost around £250 (depends on location and specialists) but blood tests can be anything from £20 to £600+.
Operations vary- think of anything from £6K- £20K for something major.
Many private hospitals have fees for operations on their websites. Most have consultant profiles and you can either contact their own PAs or ask the hospital. The way it works is that most fees are 2-tier- one for patients covered by insurance, slightly cheaper if you self-pay.
You can also sometimes mix and match- see the dr privately but if it's not urgent they can put you on their NHS list for treatment if they also work in the NHS (and not all do- some are only private.)
I guess the question is why can your GP not help? Is this too hard for them and why can't they refer you to an NHS consultant?